A053566 Expansion of (11*x-2)/(1-3*x)^2.

-2, -1, 12, 81, 378, 1539, 5832, 21141, 74358, 255879, 866052, 2893401, 9565938, 31355019, 102036672, 330024861, 1061819118, 3400690959, 10847773692, 34480423521, 109252577898, 345191655699

Offset: 0

Author

Barry E. Williams, Jan 17 2000

Keywords

• easy
• sign

References

• A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, pp. 189, 194-196.

Links

• Harvey P. Dale, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (6,-9).

Crossrefs

Cf. A023444.

Programs

GAP

List([0..30], n-> 3^(n-1)*(5*n-6)) # G. C. Greubel, May 16 2019

Magma

[3^(n-1)*(5*n-6) : n in [0..30]]; // G. C. Greubel, May 16 2019

Mathematica

LinearRecurrence[{6,-9},{-2,-1},30] (* Harvey P. Dale, Jun 26 2012 *)

PARI

Vec((11*x-2)/(1-3*x)^2 + O(x^30)) \\ Michel Marcus, Dec 03 2014

Sage

[3^(n-1)*(5*n-6) for n in (0..30)] # G. C. Greubel, May 16 2019

Formula

a(n) = 3^(n-1)*(5*n-6).

a(n) = 6*a(n-1) - 9*a(n-2), with a(0) = -2, a(1) = -1.

E.g.f.: (5*x - 2)*exp(3*x). - G. C. Greubel, May 16 2019